Abstract
In this chapter we study the main properties of the realizations of a given proper transfer function matrix \(\hat H\left( s \right) \in \mathbb{C}_p \left( s \right)^{n_o \times n_i }\). We show that the McMillan degree of Ĥ(s) is the minimal dimension of the state space of any of its realizations. We prove that two minimal realizations are algebraically equivalent. We show that eigenvalues of A of any minimal realization are dictated by the poles of Ĥ (s). We conclude this chapter with a description of a controllable canonical realization of Ĥ (s) as in [Cha. 1].
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© 1991 Springer Science+Business Media New York
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Callier, F.M., Desoer, C.A. (1991). Realization Theory. In: Linear System Theory. Springer Texts in Electrical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0957-7_13
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DOI: https://doi.org/10.1007/978-1-4612-0957-7_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6961-8
Online ISBN: 978-1-4612-0957-7
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